Interlocking interval topology explained

In mathematics, and especially general topology, the interlocking interval topology is an example of a topology on the set, i.e. the set of all positive real numbers that are not positive whole numbers.^[1]

Construction

The open sets in this topology are taken to be the whole set S, the empty set ∅, and the sets generated by

X _{n} : = \left( 0 , (1)/(n) \right) \cup (n,n +1 ) = \left\{ x \in { R} ^{+} : 0 < x < (1)/(n) or n < x < n +1 \right\}.

The sets generated by X_n will be formed by all possible unions of finite intersections of the X_n.^[2]

See also

• List of topologies

References

• Book: Steen . Lynn Arthur . Lynn Arthur Steen . Seebach . J. Arthur Jr. . J. Arthur Seebach, Jr. . . 2nd . 1978 . . Berlin, New York . 3-540-90312-7 . 507446 . 0386.54001 .

Notes and References

1. Steen & Seebach (1978) pp.77 – 78
2. Steen & Seebach (1978) p.4